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- Ron Goldman
- Computer Aided Geometric Design
- 2005

Curvature formulas for implicit curves and surfaces are derived from the classical curvature formulas in Differential Geometry for parametric curves and surfaces. These closed formulas include… (More)

- Ning Song, Ron Goldman
- Computer Aided Geometric Design
- 2009

The notion of a @m-basis for an arbitrary number of polynomials in one variable is defined. The basic properties of these @m-bases are derived, and an algorithm is presented based on Gaussian… (More)

- Thomas W. Sederberg, David C. Anderson, Ron Goldman
- Computer Vision, Graphics, and Image Processing
- 1984

Abstract The following two problems are shown to have closed-form solutions requiring only the arithmetic operations of addition, subtraction, multiplication and division: (1) Given a curve or… (More)

- Tony DeRose, Ron Goldman, Hans Hagen, Stephen Mann
- ACM Trans. Graph.
- 1993

In view of the fundamental role that functional composition plays in mathematics, it is not surprising that a variety of problems in geometric modeling can be viewed as instances of the following… (More)

- Ron Goldman, Thomas W. Sederberg, David C. Anderson
- Computer Aided Geometric Design
- 1984

In this paper vector techniques and elimination methods are combined to help resolve some classical problems in computer aided geometric design. Vector techniques are applied to derive the Bezout… (More)

- Géraldine Morin, Ron Goldman
- Computer Aided Geometric Design
- 2001

Bezier subdivision and degree elevation algorithms generate piecewise linear approximations of Bezier curves that converge to the original Bezier curve. Discrete derivatives of arbitrary order can be… (More)

- Haohao Wang, Xiaohong Jia, Ron Goldman
- Computer Aided Geometric Design
- 2009

Relationships between the singularities of rational space curves and the moving planes that follow these curves are investigated. Given a space curve C with a generic 1-1 rational parametrization… (More)

- James R. Miller, Ron Goldman
- CVGIP: Graphical Model and Image Processing
- 1995

Abstract One of the most challenging aspects of the surface-surface intersection problem is the proper disposition of degenerate configurations. Even in the domain of quadric surfaces, this problem… (More)

- Phillip J. Barry, Ron Goldman
- SIGGRAPH
- 1988

It is known that certain Catmull-Rom splines [7] interpolate their control vertices and share many properties such as affine invariance, global smoothness, and local control with B-spline curves;… (More)

- Maojie Zhang, Ron Goldman
- ISSAC
- 2000

We present a way to construct the Sylvester A-resultant matrix for three bi-degree (m, n) polynomials whose Newton polygon is modified by cutting off rectangles at the corners. We also show that the… (More)